De Rham sequences w/ knot multiplicity > 1

[vcarlier]

Enable the use of the de Rham sequence with arbitrary knots multiplicity. With this we mean that the interior knots (all knots in the periodic case) can have a constant multiplicity higher than 1.

List of modifications

• Changes in core/bsplines.py and core/bsplines_kernels.py :

  • Modify the make_knots function to create an appropriate knot sequence in all cases. In the non periodic case the interior knots are repeated multiplicity times and the boundary knots p+1 times. In the periodic case, interior knots are repeated multiplicity times and we add p+1 knots at each side by periodicity. In all cases the number of knots is (n_cells-1) * multiplicity + 2 * (p+1).
  • Modify functions collocation_matrix and histopolation_matrix to take in account that now in the periodic case the number of basis function is len(knots) - 2 * (p+1) + multiplicity.
  • Modify greville function for the maximum multiplicity case to avoid having the discontinuity points of the spline.

• Changes in modules psydac.feec.derivatives and psydac.feec.global_projectors to take in account that the ghost regions have size shifts * pads (previously was pads)

• Changes in psydac.fem.splines: repercussion of the changes in psydac.core.bsplines, adding multiplicity as argument to several functions. Correct the computation of the multiplicity from the knot sequence.

• Add tests in feec/tests/test_differentiation_matrices.py and feec/tests/test_global_projectors.py with higher multiplicity.

• Add test in api/tests/tests_api_feec_1d.py, api/tests/tests_api_feec_2d.py, api/tests/tests_api_feec_3d.py with higher multiplicity.

[yguclu]

Looks good to me! I have only minor comments

[yguclu]

@campospinto Do you have any further comments or questions on this PR?

[campospinto]

@campospinto Do you have any further comments or questions on this PR?

Just one minor suggestion ! Otherwise it looks good, thanks !